BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

#220 from the OG PS section

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Legendary Member
Posts: 566
Joined: Fri Jan 04, 2008 11:01 am
Location: Philadelphia
Thanked: 31 times
GMAT Score:640

#220 from the OG PS section

by AleksandrM » Mon Apr 21, 2008 6:37 pm
John and Mary were each paid x dollars in advance to do a certain job together. John worked on the job for 10 hours and Mary worked 2 hours less than John. If Mary gave John y dollars of her payment so that they would have received the same hourly wage, what was the dollar amount, in terms of y, that John was paid in advance?

A) 4y
B) 5y
C) 6y
D) 8y
E) 9y

Here is how I decided to solve this problem:

x = $10

This means that John's hourly wage was $1 and Mary's was $1.25 [since she worked 8 hours].

Now, in order for john to have the same wage as Mary, he needs to of been given y dollars, which is what?

x/10 = 1.25 ----> x = 12.50, which means that y = 2.5

Then, I substituted y into C, which did not work, then into B, which gave me 12.50.

However, that is the wrong answer. Curious to know where I went wrong using this method [I suspect the failure is in the exchange of the 2.50, which would cause Mary's wage to decrease to about 94 cents]. Help is appreciated, as always.
Top
Source: — Problem Solving |
Senior | Next Rank: 100 Posts
Posts: 77
Joined: Thu Apr 10, 2008 10:13 pm
Thanked: 4 times

by akshatsingh » Mon Apr 21, 2008 7:59 pm
John and Mary were each paid x dollars in advance to do a certain job together. John worked on the job for 10 hours and Mary worked 2 hours less than John. If Mary gave John y dollars of her payment so that they would have received the same hourly wage, what was the dollar amount, in terms of y, that John was paid in advance?


My Solution:
John's per hour payment= x/10
Mary's per hour payment= x/8
Mary gave John y dollars so that they would have received the same hourly wage, that means,

(x-y)/8=(x+y)/10
5(x-y)=4(x+y)
x=9y
As the question asks what was John paid in advance..

My answer would be 9y

Cheers!
Aks
Top
User avatar
Legendary Member
Posts: 986
Joined: Wed Dec 20, 2006 11:07 am
Location: India
Thanked: 51 times
Followed by:1 members

Re: #220 from the OG PS section

by gabriel » Tue Apr 22, 2008 1:36 am
AleksandrM wrote:John and Mary were each paid x dollars in advance to do a certain job together. John worked on the job for 10 hours and Mary worked 2 hours less than John. If Mary gave John y dollars of her payment so that they would have received the same hourly wage, what was the dollar amount, in terms of y, that John was paid in advance?

A) 4y
B) 5y
C) 6y
D) 8y
E) 9y

Here is how I decided to solve this problem:

x = $10

This means that John's hourly wage was $1 and Mary's was $1.25 [since she worked 8 hours].

Now, in order for john to have the same wage as Mary, he needs to of been given y dollars, which is what?
You have it right till here...

AleksandrM wrote: x/10 = 1.25 ----> x = 12.50, which means that y = 2.5

Then, I substituted y into C, which did not work, then into B, which gave me 12.50.

However, that is the wrong answer. Curious to know where I went wrong using this method [I suspect the failure is in the exchange of the 2.50, which would cause Mary's wage to decrease to about 94 cents]. Help is appreciated, as always.
This is the part where you go wrong. You assume that even after the money is exchanged the hourly wage remains the same. Remember that when Mary gives John "y" dollars the total money received by John increases and the total money received by Mary decreases, this in turn means that the hourly money received by John increases and that received by Mary decreases.

So your equation should be "hourly money received by john" = "hourly money received by Mary"

That is (10+y)/10 = (10-y)/8 .. solve for y and you should get your answer ... which btw is E ..
Top
User avatar
Legendary Member
Posts: 566
Joined: Fri Jan 04, 2008 11:01 am
Location: Philadelphia
Thanked: 31 times
GMAT Score:640

by AleksandrM » Tue Apr 22, 2008 9:31 am
I would say that this is a pretty difficult problem because of the number of steps involved. I have used the plug-in method for easier problems, and have been able to use the "target number" approach with those. However, for this, it is good to plug in the numbers in order to visualize it, but better to solve it using algebra once you understand it. That, at least, is my feeling about it. Thank you both for your input.
Top
Legendary Member
Posts: 631
Joined: Mon Feb 18, 2008 11:57 pm
Thanked: 29 times
Followed by:3 members

Re: #220 from the OG PS section

by netigen » Tue Apr 22, 2008 9:58 am
gabriel wrote:
AleksandrM wrote:John and Mary were each paid x dollars in advance to do a certain job together. John worked on the job for 10 hours and Mary worked 2 hours less than John. If Mary gave John y dollars of her payment so that they would have received the same hourly wage, what was the dollar amount, in terms of y, that John was paid in advance?

A) 4y
B) 5y
C) 6y
D) 8y
E) 9y

Here is how I decided to solve this problem:

x = $10

This means that John's hourly wage was $1 and Mary's was $1.25 [since she worked 8 hours].

Now, in order for john to have the same wage as Mary, he needs to of been given y dollars, which is what?
You have it right till here...

AleksandrM wrote: x/10 = 1.25 ----> x = 12.50, which means that y = 2.5

Then, I substituted y into C, which did not work, then into B, which gave me 12.50.

However, that is the wrong answer. Curious to know where I went wrong using this method [I suspect the failure is in the exchange of the 2.50, which would cause Mary's wage to decrease to about 94 cents]. Help is appreciated, as always.
This is the part where you go wrong. You assume that even after the money is exchanged the hourly wage remains the same. Remember that when Mary gives John "y" dollars the total money received by John increases and the total money received by Mary decreases, this in turn means that the hourly money received by John increases and that received by Mary decreases.

So your equation should be "hourly money received by john" = "hourly money received by Mary"

That is (10+y)/10 = (10-y)/8 .. solve for y and you should get your answer ... which btw is E ..
Actually after the exchange the hourly rate becomes the same.

It was not the same before the exchange because both were paid the same amount X for different no. of hours of work
Top
User avatar
Legendary Member
Posts: 986
Joined: Wed Dec 20, 2006 11:07 am
Location: India
Thanked: 51 times
Followed by:1 members

Re: #220 from the OG PS section

by gabriel » Wed Apr 23, 2008 3:35 am
netigen wrote: ..
Actually after the exchange the hourly rate becomes the same.

It was not the same before the exchange because both were paid the same amount X for different no. of hours of work
Isnt that what I said :) . What I meant was that the hourly level does not remain the same i.e. their previous levels of wages does not remain same. I did not mean that Mary and John's hourly wage was the same before the exchange.
Top
Master | Next Rank: 500 Posts
Posts: 140
Joined: Sat Feb 28, 2009 8:51 am
Location: India
Thanked: 14 times
Followed by:3 members

Re: #220 from the OG PS section

by farooq » Sat Oct 24, 2009 10:00 pm
John and Mary were each paid x dollars in advance to do a certain job together. John worked on the job for 10 hours and Mary worked 2 hours less than John. If Mary gave John y dollars of her payment so that they would have received the same hourly wage, what was the dollar amount, in terms of y, that John was paid in advance?

A) 4y
B) 5y
C) 6y
D) 8y
E) 9y
Let assume $80 paid to each.

John received $80 for 10 hrs work..therefore John per hour charge is $8

Mary also receive $80 but for 8 hrs...therefore Mary's per hour charge is $10.

No may has to give few dollars to john so both of them have equal amount.

8....10
make it equal....
9.....9 (Mary gives 1 dollar to John)

Finally, John amount should be multiple of 9. D is correct.
Regards,
Farooq Farooqui.
London. UK

It is your Attitude, not your Aptitude, that determines your Altitude.
Top
Newbie | Next Rank: 10 Posts
Posts: 5
Joined: Sat Jul 18, 2009 7:39 pm

by leo700 » Thu Dec 24, 2009 10:49 am
I used the same approach than farooq, however D is not a multiple of 9, so E is the answer
Top
Post new topic Post Reply
• Page 1 of 1